Creating skyrmions and skyrmioniums using oscillating perpendicular magnetic fields

Highlights

• A perpendicular oscillating magnetic field can be used to create a skyrmion or a skyrmionium.

• Rapid creation of skyrmions and skyrmioniums in the sub nanoseconds time range.

• Selective creation of skyrmions or skyrmioniums, depending on the envisaged application.

Abstract

Magnetic skyrmions and skyrmioniums are exotic magnetic configurations that have several potential applications in Spintronics. In this work, using micromagnetic simulations, we show that it is possible to create metastable skyrmions and skyrmioniums in an isolated cobalt nanodisk, that has as its minimum energy configuration a single domain with perpendicular magnetization. First, we have determined the ground state of the nanodisk and the frequencies of the spin wave modes of skyrmions and skyrmioniums for different values of perpendicular uniaxial anisotropy constant $K_{\mathrm{z}}$ and Dzyaloshinskii-Moriya exchange constant $D_{\mathrm{int}}$. Next, in order to create a skyrmion or skyrmionium, we have applied an oscillating perpendicular magnetic field with a frequency equal to that of the spin wave modes. Our results show that it is possible to switch from single domain to skyrmion or skyrmionium, tuning parameters such as the intensity of the applied perpendicular magnetic field, and its duration.

Introduction

Non-trivial topologically protected spin textures, such as magnetic skyrmions, can be created in ferromagnetic nanostructures with different geometries [1], [2], [3], [4], [5], [6], [7]. Magnetic skyrmions are characterized by the topological charge Q. For skyrmions with polarity p = +1, i.e., magnetization at the center in the +z direction, the topological charge is Q = 1, and for skyrmions with polarity p = −1, the topological charge is Q = −1 [6], [8].

The topological protection of magnetic skyrmions allows them to evade obstacles or defects in the nanostructures as they move [9], and also coexist in the form of clusters, without mutual annihilation [10]. Magnetic skyrmions can be moved with small current densities [8], reducing the undesirable Joule heating that is detrimental in Spintronics applications, e.g., racetrack memories [11].

Skyrmioniums, also called target skyrmions [12] or 2$\pi$-skyrmions [13], are another type of spin texture similar to skyrmions, that can also be created in ferromagnetic nanostructures [14], [15], [16], [12], [17], [18]. A skyrmionium can be considered as a combination of two skyrmions with opposite topological charge [17], [12], resulting in a total topological charge Q = 0. This allows the skyrmionium, unlike the skyrmion, to move without suffering deflections due to the skyrmion Hall effect (SkHE). This property is essential to read and write information in potential applications of skyrmioniums as components of devices for magnetic recording [18].

Skyrmioniums can reach higher velocities in comparison with a skyrmion [19], [17], another property that is relevant for applications in Spintronics.

Skyrmioniums in magnetic nanostructures arise in micromagnetic simulations [20], [15], [21] and have been experimentally observed at low temperature and room temperature [12], [22], [23], [24]. They can be created in ferromagnetic nanostructures by tuning parameters such as the ratio of the thickness to the radius of the nanodisk, perpendicular magnetic anisotropy, and Dzyaloshinskii-Moriya interaction [20], or using an external perturbation, e.g., spin polarized current [15], and static perpendicular magnetic field [25], [14], [12].

However, it is necessary to look for methods that allow us to have selectivity in creating either magnetic skyrmions, or skyrmioniums, in an isolated nanostructure.

In the present work, we propose a simple method to create selectively these textures, in a nanodisk with a perpendicularly magnetized single-domain, using oscillating perpendicular magnetic fields with frequencies equal to the frequencies of the spin wave modes of these textures. To demonstrate this idea, we used the open source code Mumax3 [26], with a cell size 1 $\times$ 1 $\times$ L nm³, where L is the thickness of the nanodisk. We assumed T = 0 K, however, the present method is valid at room temperature (see Supplementary material). The material used was Cobalt with parameters [20], [27]: saturation magnetization ${\mathrm{M}}_s$ = 5.8 $\times$ ${10}^5$A/m, exchange stiffness ${\mathrm{A}}_{\mathit{ex}}$ = 15 pJ/m, perpendicular uniaxial anisotropy constant $K_{\mathrm{z}}$ = 0.8 and 1.0 MJ/m³, and Dzyaloshinskii-Moriya exchange constant $D_{\mathrm{int}}$ ranging between 3.4 and 4.0 mJ/m².